10th Class Mathematics 3rd Quarter Book Paper

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

1. Which of the following vectors represents a position vector?
   1. $\overrightarrow{OP}$
   2. $-\overrightarrow{OP}$
   3. $\overrightarrow{PO}$
   4. $\overrightarrow{PQ}$
2. If a circle is divided into ten equal arcs, then central angle of each arc is …………
   1. 10°
   2. 36°
   3. 60°
   4. 90°
3. In right △ABC, a = 2 cm , c = 4 cm, what is α?
   1. 30°
   2. 45°
   3. 60°
   4. 120°
4. Given that $\vec{u}$ is any vector. Which of the following is true?
   1. $$\left| -\vec{u} \right| = \left| \vec{u} \right|$$
   2. $$-\left| \vec{u} \right| = \left| \vec{u} \right|$$
   3. $$\left| \vec{u} \right| = \left| -\vec{u} \right|$$
   4. $$| \vec{u}| = 0$$
5. Corresponding arcs of two congruent chords of a circle are …………
   1. unequal
   2. major
   3. congruent
   4. minor
6. For an equilateral triangle, r : r1 : R =
   1. 1: 2 : 3
   2. 3: 2 : 1
   3. 1: 1 : 2
   4. 1: 3 : 2
7. If $\overrightarrow{OP}$= [-6 , 7] , then $-\overrightarrow{OP}$ is equal to
   1. [-6 , 7]
   2. [6 , 7]
   3. [6 , -7]
   4. [-6 , -7]
8. An angle whose vertex is centre of circle and whose arms pass through end points of an arc is known as ………… angle.
   1. inscribed
   2. central
   3. interior
   4. exterior
9. If a , a and b are length sides of an isosceles triangle, then S = . . .
   1. $\frac{a}{2} + b$
   2. $a + \frac{a +b}{2}$
   3. $a - \frac{a +b}{2}$
   4. $a + \frac{b}{2}$
10. If $\vec{u} = [-5x , 8]$ and $\vec{v} = [10 , 4y]$ are equal vectors, then:
    1. x = 2 , y = 2
    2. x = -2 , y = -2
    3. x = -2 , y = 2
    4. x = 2 , y = -2
11. In the figure, AB = 4 cm, OC = 3 cm. Chord DE passes through mid of OC and is parallel to AB. What is the length of DE?
    1. 4.5 cm
    2. 5.6 cm
    3. 6.6 cm
    4. 3.3 cm
12. Area of an equilateral triangle having side a is:
    1. $\frac{\sqrt{3}}{8}a$
    2. $\frac{\sqrt{3}}{4}a^2$
    3. $\frac{\sqrt{3}}{16}a^2$
    4. $\frac{\sqrt{3}}{16}a$